He was a child prodigy, publishing his first paper at 15. Now Stephen Wolfram says he has created a new kind of science based on simple computer programs rather than equations. It鈥檚 a bold claim, but it has taken him 20 years-ten of them thinking and working late into the night, and publishing nothing. By a nice irony, that intellectual space was bought by the millions he made out of Mathematica, a computer program that makes complicated mathematics doable for ordinary mortals. Now, at 41, he鈥檚 busy gearing himself up for the glare of publicity as he prepares to publish the fruit of all those years. Marcus Chown caught up with Wolfram-at 3 am.
Are you the Isaac Newton of the 21st century?
Who knows? I think I鈥檝e discovered some big and important things. But I鈥檓 more interested in what I鈥檝e discovered than where it puts me in the world. Sometimes I think I might be happier just to figure things out and keep them to myself. I鈥檝e put a lot of effort into getting ready to share them. And if people actually start to understand what I鈥檝e figured out, then I think I鈥檒l be forced to be a very famous scientist. I have mixed feelings about that. But I think it鈥檚 important to the ideas that I don鈥檛 try to avoid it too much.
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What鈥檚 the story behind this new kind of science? How did it all begin?
Around 1980, I had become interested in several really different questions-galaxy formation and how brains work. They all seemed to be getting stuck in the same kind of way. I began to realise that the real problem was with the basic infrastructure of science. For about 300 years, most of science has been dominated by the idea of using mathematical equations to model nature. That worked really well for Newton and friends, figuring out orbits of planets and things, but it鈥檚 never really worked with more complicated phenomena in physics, such as fluid turbulence. And in biology it鈥檚 been pretty hopeless.
If equations aren鈥檛 the right infrastructure for modelling the world, what is?
Simple programs. If you鈥檙e going to be able to make scientific theories at all, systems in nature had better follow definite rules. But why should those rules be based on the constructs of human mathematics? In the past, there wasn鈥檛 any framework for thinking about more general kinds of rules. But now you can think of them as being like computer programs. About 20 years ago, I decided to try to work out what kind of science you could build from these more general kinds of rules. The first big question was what do these rules typically do? What do simple programs typically do?
Did you carry out experiments to find out?
Yes. I started with very simple programs called cellular automata. The version that I used began with a row of cells, each either black or white. Then you make a new row underneath. You use a definite rule to work out the colour of each cell, by looking at the colours of its neighbours on the row above. And then you repeat this over and over again. It鈥檚 a simple set-up. There are just 256 of these kinds of programs. The question is what happens when you run them, say just starting with a single black cell. You would guess it should always be something simple. The remarkable thing I discovered-almost 20 years ago-is that this intuition is completely wrong. You see, of the 256 possible cellular automata, several make incredibly complicated patterns that look almost completely random and that you鈥檇 never imagine came just from repeatedly applying a simple rule to a single black square.
So your experiments convinced you that nature uses simple programs to generate the complexity we see around us鈥�
Yes, I think it鈥檚 the main secret of nature. It鈥檚 what lets nature come up with things that look so much more complex than anything we鈥檝e been able to invent does. Some people say complexity in biology can鈥檛 just be coming from natural selection. They鈥檙e right, but the point is that nature uses tools we didn鈥檛 expect. That鈥檚 what I鈥檝e discovered.
How did you follow up on this?
I worked out lots of details and published lots of papers. And I got lots of other people interested. The whole topic of complexity got very popular. I even began a journal and a research centre. But people understood only part of what I鈥檇 done. The rest required a big conceptual leap. And if you want to pursue those things, history says you pretty much have to go it alone.
And a new science needs a new tool-was that why you invented Mathematica?
Partly. I needed to be able to build programs then find out what they do as efficiently as possible. It required big new ideas about setting up software systems to do that. It turned out that the very fact that I could figure out how to build all the complexity of Mathematica from quite simple 鈥減rimitives鈥� was an important inspiration. It made me realise that I might work out what primitives nature uses for its rules. So Mathematica was both a tool and an inspiration.
What exactly does Mathematica do?
It鈥檚 a complete environment for technical computing. It lets people do a huge range of calculations, and creates graphics and documents, interacts with the Web, and so on. It鈥檚 all based on a language that lets you build complex programs far more easily than before. A few million people use it.
Did that make you a multimillionaire?
Yes, I鈥檝e made a lot of money, but I鈥檝e always wanted to put my energies into the things that I find most interesting. What motivates me most is discovering new things and building new ideas.
Tell me about your 10 years of silence鈥�
It began in 1991 after I鈥檇 built up a terrific team at my company. I began to split my time between management and basic science. I wanted to finish building the new kind of science I鈥檇 begun in the early 1980s. I had no idea it would take so long. I kept on discovering more and more things. Every time I turned over a rock there was a huge new universe underneath. It鈥檚 been exciting, but there鈥檚 been a huge amount to do and it鈥檚 taken immense focus to get it all done. I always used to like lecturing and travelling, but to get this project done, I鈥檝e had to shut those kinds of things down.
And talking to journalists?
Right. I鈥檓 going to have to get used to that again now.
So, what have you discovered?
Enough to fill hundreds-maybe thousands-of scientific papers. I鈥檝e amassed a huge amount of evidence for my idea that simple programs-like the cellular automata-are the key to lots of important phenomena in nature. In physics, for instance, I can finally explain why the second law of thermodynamics works-that is, why many physical systems tend to become irreversibly more random as time progresses. In biology, I now know how a lot of the complexity arises. I鈥檝e discovered that many things we might have thought were special about life and intelligence, for example, can also emerge in all kinds of physical systems. Consequently, I don鈥檛 believe 鈥渁nthropic鈥� arguments that say that for us to be here it鈥檚 necessary for there to be stars, galaxies and so on. There can be things just as complex as us without any of that.
Why haven鈥檛 you published any of this?
Because it鈥檚 all part of a big picture that can be communicated properly only by showing everything together. I guess if someone else had been paying for my work, I might have had to give progress reports. Fortunately, I鈥檝e been able to concentrate on putting everything together in a nice coherent way, as a book called A New Kind of Science. It鈥檚 been a huge project. I鈥檝e devoted about 100 million keystrokes to it. I鈥檝e taken a lot of trouble to polish my ideas so they鈥檙e as clean as possible. Usually, new directions in science begin far more gradually, with lots of people involved. But the things I鈥檓 doing now are different enough that I鈥檝e had to build up a whole new intellectual structure by myself.
Who鈥檚 the book aimed at?
Everyone. It鈥檚 completely new so there aren鈥檛 any specialists. It may turn out that people who have good intellectual discipline but perhaps don鈥檛 know so much about science will have an easier time.
Have you discovered the simple program that is generating the Universe?
Not yet. But I have found increasing evidence that it exists. It could be as simple as a few lines of Mathematica code. I think before too many years it鈥檒l be possible to find it.
So is Stephen Hawking right about scientists being close to discovering a 鈥渢heory of everything鈥�?
Well, the things I鈥檝e been thinking about are very, very different from the usual quantum field theory and string theory approach. There鈥檚 some very basic intuition that鈥檚 different when you think about simple programs instead of equations and so on. One big issue is that getting a fundamental theory of physics doesn鈥檛 mean physics is finished. That鈥檇 be like saying that computing is finished once you have a computer. Suppose that the program for the Universe is four lines long. There鈥檚 no room in those four lines to put in all the familiar stuff we know about space-time having four dimensions, the muon being 206 times the mass of the electron, and so on. Almost nothing from the everyday world will be obvious in the program. These things will have to emerge when the program runs. Figuring out how that works, and exactly what can emerge, can be arbitrarily difficult.
Could it be that the Universe-generating program will only produce what we see around us after it鈥檚 run for 13 billion years?
Yes, I think that will be partly true. But even though the evolution of the Universe as a whole may be what I call computationally irreducible, there will still be patches that are reducible-where we can figure what the Universe does faster than it does it. And actually almost all of what traditional equation-based science has been doing is looking just at those computationally reducible parts.
So there鈥檚 no mystery in Einstein鈥檚 famous observation that the most incomprehensible thing about the Universe is that it鈥檚 comprehensible?
Well, I think that鈥檚 really much more a statement about the practice of science than about our Universe. One of the clear lessons from history is that fields of science tend to get defined according to whatever their methods allow them to study successfully. What I鈥檝e discovered is that there鈥檚 lots of other stuff out there that you can see if you think in terms of programs.
So if the Babylonians had invented computer programs before geometry, might science have been more effective?
Well, quite a bit of what I鈥檝e discovered could have been found by the Babylonians. If you know what to look for, you could just find it by arranging pebbles with a simple rule. Young kids today could certainly do it. If my kind of science had been around for ages, perhaps only now would a Newton have invented calculus.